Solve the following inequalities and express the answer in interval notation.

• A. $\(\left\]\lbrack\)4,10\(\right\))$
• B. $\(\left\)(4,10\(\right\]\rbrack\)$
• C. $\(\left\]\lbrack\)0,6\(\right\))$
• D. $\(\left\)(0,6\(\right\]\rbrack\)$

Answer: (B)

Verified step by step guidance

1. Start with the compound inequality: \(1 < \frac{x - 2}{2} \leq 4\).
2. To eliminate the fraction, multiply all parts of the inequality by 2 (which is positive, so the inequality signs remain the same): \(2 \times 1 < 2 \times \frac{x - 2}{2} \leq 2 \times 4\).
3. Simplify each part: \(2 < x - 2 \leq 8\).
4. Next, isolate \(x\) by adding 2 to all parts of the inequality: \(2 + 2 < x - 2 + 2 \leq 8 + 2\).
5. Simplify the inequality to get the solution range for \(x\): \(4 < x \leq 10\). Express this solution in interval notation as \((4, 10]\).